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Video semantic segmentation (VSS) is beneficial for dealing with dynamic scenes due to the continuous property of the real-world environment. On the one hand, some methods alleviate the predicted inconsistent problem between continuous frames. On the other hand, other methods employ the previous frame as the prior information to assist in segmenting the current frame. Although the previous methods achieve superior performances on the independent and identically distributed (i.i.d) data, they can not generalize well on other unseen domains. Thus, we explore a new task, the video generalizable semantic segmentation (VGSS) task that considers both continuous frames and domain generalization. In this paper, we propose a class-wise non-salient region generalized (CNSG) framework for the VGSS task. Concretely, we first define the class-wise non-salient feature, which describes features of the class-wise non-salient region that carry more generalizable information. Then, we propose a class-wise non-salient feature reasoning strategy to select and enhance the most generalized channels adaptively. Finally, we propose an inter-frame non-salient centroid alignment loss to alleviate the predicted inconsistent problem in the VGSS task. We also extend our video-based framework to the image-based generalizable semantic segmentation (IGSS) task. Experiments demonstrate that our CNSG framework yields significant improvement in the VGSS and IGSS tasks.